SOLUTION: a fort is provisioned for 42 days; after 10 days a reinforcement of 200 men arrives and the food will now last only for 24 days . how many men were there in the fort?

Question 317452: a fort is provisioned for 42 days; after 10 days a reinforcement of 200 men arrives and the food will now last only for 24 days . how many men were there in the fort?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A fort is provisioned for 42 days ; after 10 days a reinforcement of 200 men arrives and the food will now last only for 24 days . how many men were there in the fort?
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Let original number of men in the fort = "x".
(food in fort)/x = 42 days
(ff)/42 = x
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After 10 days:
Amt of original food remaining = (32/42)(ff) = (16/21)ff
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Equation:
(16/21)(ff)/(x+200) = 24
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Substitute for (ff) and solve for "x":
(16/21)(42x)/(x+200) = 24
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16(2x) = 24x + 4800
32x = 24x + 4800
8x = 4800
x = 600 men (number of men in the fort before 200 more arrived)
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Cheers,
Stan H.
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